Concrete Abstract Algebra: From Numbers to Gröbner Bases

by Niels Lauritzen

Overview

Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gr"obner bases, while takin in all the usual material of a traditional introductory course. In addition, there is a rich supply of topics such as cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials, and systems of non-linear equations. A special feature is that Gr"obner bases do not appear as an isolated example. They are fully integrated as a subject that can be successfully taught in an undergraduate context. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications, and exercises. The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts. This book is built on several years of experienced teaching introductory abstract algebra at Aarhus, where the emphasis on concrete and inspiring examples has improved student performance significantly.

Product Details

ISBN-13:	9780521826792
Publisher:	Cambridge University Press
Publication date:	10/16/2003
Pages:	256
Product dimensions:	6.00(w) x 9.10(h) x 0.70(d)

Table of Contents

1. Numbers; 2. Groups; 3. Rings; 4. Polynomials; 5. Gröbner bases.

Editorial Reviews

"Lauritzen does a great job of motivating the concepts covered. The title of the book seems to be contradictory, but after reading the book, you will really have the feeling that Lauritzen achieved his goal: to concretize the abstract without losing rigor and depth. The text is very readable, and the well-chosen exercises help the reader understand the material. I highly recommend this book as a text for teaching abstract algebra. If you are looking for a solid introduction to the topic of abstract algebra, this is the book for you." Computing Reviews

From the Publisher